Difference-in-Discontinuities: Estimation, Inference and Validity Tests (2405.18531v1)

Abstract: This paper investigates the econometric theory behind the newly developed difference-in-discontinuities design (DiDC). Despite its increasing use in applied research, there are currently limited studies of its properties. The method combines elements of regression discontinuity (RDD) and difference-in-differences (DiD) designs, allowing researchers to eliminate the effects of potential confounders at the discontinuity. We formalize the difference-in-discontinuity theory by stating the identification assumptions and proposing a nonparametric estimator, deriving its asymptotic properties and examining the scenarios in which the DiDC has desirable bias properties when compared to the standard RDD. We also provide comprehensive tests for one of the identification assumption of the DiDC. Monte Carlo simulation studies show that the estimators have good performance in finite samples. Finally, we revisit Grembi et al. (2016), that studies the effects of relaxing fiscal rules on public finance outcomes in Italian municipalities. The results show that the proposed estimator exhibits substantially smaller confidence intervals for the estimated effects.

• The paper introduces the Difference-in-Discontinuities design that merges DiD and RDD frameworks to enhance causal effect estimation.
• It develops a nonparametric estimator with rigorous asymptotic analysis and validity tests to minimize bias from time-varying confounders.
• Monte Carlo simulations and an empirical case study demonstrate its enhanced precision, yielding narrower confidence intervals than traditional methods.

An Examination of Difference-in-Discontinuities: Estimation, Inference, and Validity Tests

The paper "Difference-in-Discontinuities: Estimation, Inference, and Validity Tests" by Pedro Picchetti, Cristine C. X. Pinto, and Stéphanie T. Shinoki introduces an econometric approach aimed at addressing the limitations of traditional Difference-in-Differences (DiD) and Regression Discontinuity Design (RDD) methodologies. Typically employed in the analysis of causal effects using observational data, these methodologies can falter when certain assumptions, such as parallel trends in DiD or time-invariant outcomes at the cutoff in RDD, are not met. The proposed Difference-in-Discontinuities (DiDC) design merges aspects of both methodologies, promising more robust results particularly in complex scenarios involving time-variant confounders.

Overview and Methodology

The paper begins by formalizing the DiDC design, which evaluates treatment effects by leveraging temporal variations across a discontinuity. This approach is particularly compelling when pre-existing discontinuities confound traditional RDD analysis, or when varied trends jeopardize the typical use of DiD. The authors rigorously define identification assumptions crucial for the validity of DiDC, which includes conditions under which pre-existing confounding effects remain constant over time and independently affect the primary treatment in question.

The authors propose a nonparametric estimator for the DiDC and delve deeply into its asymptotic properties. By deriving conditions under which the DiDC biases are minimized, the authors suggest that their methodology can provide more accurate estimates than standard RDD, especially in scenarios with confounders unknown at the time of analysis. Furthermore, they introduce a comprehensive suite of validity tests designed to bolster confidence in the estimation results by empirically testing crucial assumptions within the DiDC framework.

Numerical Simulations and Case Study

The performance of these estimators is illustrated through Monte Carlo simulations, revealing noteworthy findings. Specifically, the simulations demonstrate that DiDC estimators achieve improved estimation accuracy, yielding results with reduced bias and favorable confidence interval coverage compared to approaches that do not account for confounding and changing economic environments. Adding credence to these findings, the authors revisit an empirical analysis from Grembi et al. (2016), regarding fiscal rules in Italian municipalities, applying their DiDC estimator. The evidence from this case paper indicates that DiDC provides narrower confidence intervals, potentially illustrating enhanced estimation precision.

Implications and Future Directions

The DiDC design and its affiliated methodology present theoretical implications for econometricians interested in more accurately identifying treatment effects in the presence of complex confounders. Practical application is perhaps most critical to researchers in fields such as economics, where observational data remain a cornerstone of substantive empirical work. The DiDC design could fundamentally alter approaches to causal inference, providing the ability to integrate time-series and panel data more effectively.

The theoretical underpinnings outlined in this paper suggest several avenues for future research. Investigating the sensitivity of the results to different kinds of econometric assumptions, especially concerning the form of bias correction algorithms, presents one such area. Furthermore, as real-world applications of DiDC grow, refined methodologies for determining the optimal bandwidth choices will be indispensable. These developments could enhance the utility of DiDC across a broader range of economic and social phenomena.

Conclusion

The paper establishes a substantive enhancement to existing econometric designs, offering a powerful tool to researchers confronted with the challenge of confounded causal inference amid time-variant effects. By merging the RDD and DiD frameworks, the authors provide a flexible and sophisticated approach that has the potential to rigorously improve empirical investigations in economics and related fields. As researchers continue to refine and apply the DiDC design, it seems poised to become an essential component of empirical econometric toolkits.